Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×#106×C47 ⋊ C2 |
| Sylow | C47 ⋊ #2079 |
198 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 63 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,47|a^2=eg,c^2=d,e^2=g,f^2=g,b^a=bd,c^a=ce,c^b=cf,f^b=fg,h^b=h^46,e^c=eg,f^c=fg670 conjugacy classes — view the full character table.
| maximal subgroup of | D47×#2079, C2×#20244834, #26245181, … |
| maximal normal subgroup of | D47×#2079, C2×#20244834, #26245181, … |
| maximal quotient of | #26120999, #26121006, #26121013, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 5956);